In the setting of finite reflection groups, we prove that the projection of a Brownian motion onto a closed Weyl chamber is another Brownian motion normally reflected on the walls of the chamber. Our proof is probabilistic and the decomposition we obtain may be seen as a multidimensional extension of Tanaka's formula for linear Brownian motion. The paper is closed with a description of the boundary process through the local times of the distances from the initial process to the facets.
Cite this article
Nizar Demni, Dominique Lépingle, Brownian Motion, Reflection Groups and Tanaka Formula. Rend. Sem. Mat. Univ. Padova 127 (2012), pp. 41–55